Comparing ATG or Post-Transplant Cyclophosphamide to Calcineurin Inhibitor-Methotrexate as GVHD Prophylaxis After Myeloablative Unrelated Donor Peripheral Blood Stem Cell Transplantation

OUTLINE: CONDITIONING REGIMENS: Participants receive 1 of 3 regimens and are randomized to 1 of 3 arms for GVHD prophylaxis. REGIMEN A: Participants undergo total body irradiation (TBI) twice daily (BID) on days ‐6 to ‐4 (‐7 to ‐4 for those < 18 years), then receive cyclophosphamide IV over 1‐2 hours on days ‐3 and ‐2. Participants randomized to Arm 2 only receive TBI on days ‐3 to ‐1 (‐4 to ‐1 for those < 18 years). REGIMEN B: Participants receive fludarabine phosphate IV and busulfan IV every 6 hours on days ‐5 to ‐2. REGIMEN C: Participants receive busulfan orally (PO) or IV every 6 hours on days ‐7 to ‐4 and cyclophosphamide IV over 1‐2 hours on days ‐3 and ‐2. Myelofibrosis or other myeloproliferative neoplasms: Participants >= 18 years receive cyclophosphamide IV over 1‐2 hours on days ‐7 and ‐6 and busulfan IV on days ‐5 to ‐2. Participants < 17 years receive busulfan IV every 6 hours on days ‐7 to ‐4 and cyclophosphamide IV on days ‐3 and ‐2. All participants undergo peripheral blood stem cell transplantation on day 0. ARM 1: Participants receive anti‐thymocyte globulin IV over 4‐6 hours on days ‐3 to ‐1. Beginning day ‐1, participants also receive tacrolimus IV or cyclosporine IV twice daily (BID) tapered at day 50, and methotrexate IV on days 1, 3, 6 and 11 in the absence of disease progression or unacceptable toxicity. ARM 2: Participants receive cyclophosphamide IV over 1‐2 hours on days 3 and 4. Beginning day 5, participants also receive tacrolimus IV or cyclosporine IV BID tapered at day 50 in the absence of disease progression or unacceptable toxicity. ARM 3: Beginning day ‐1, participants receive tacrolimus IV or cyclosporine IV BID tapered at day 50, and methotrexate IV on days 1, 3, 6 and 11 in the absence of disease progression or unacceptable toxicity. After completion of study treatment, participants are followed up at 6 months, then annually up to 5 years.